57.3.5 problem 5

Internal problem ID [9062]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 5
Date solved : Monday, January 27, 2025 at 05:31:47 PM
CAS classification : [_separable]

\begin{align*} t y^{\prime }+y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (x_{0} \right )&=y_{0} \end{align*}

✓ Solution by Maple

Time used: 1.436 (sec). Leaf size: 10

dsolve([t*diff(y(t),t)+y(t)=0,y(x__0) = y__0],y(t), singsol=all)
 

\[ y = \frac {y_{0} x_{0}}{t} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 11

DSolve[{t*D[y[t],t]+y[t]==0,y[x0]==y0},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\text {x0} \text {y0}}{t} \]